2013-05-29

saving Kepler, calibrating Kepler

Fergus, Schölkopf, Foreman-Mackey, Fadely, and I (yes, most of CampHogg) had a big free-for-all on how we might (first) make current Kepler lightcurve data more precise, and (second) develop calibration and photometry systems that would permit Kepler to operate in radical modes if it is stuck with only two reaction wheels going forward. On the second point, we didn't get very far, except to decide that if the things the Kepler team is currently trying fail, we will chime in with the suggestion that some observing modes that they might be ruling out out of hand (for perfectly sensible reasons) might still be scientifically useful, if they are accompanied by a very hard-core calibration scheme.

On the first point, Fergus wrote down a full causal generative model for the Kepler data under weak assumptions, and then I linearized it (possible because pointing and temperature variations are small in relevant units). We found out that every light curve ought to be expressible as a true light curve times a linear function of spacecraft attitude and temperature perturbations, plus another linear function of spacecraft attitude and temperature perturbations. This is a kind of matrix factorization; in the limit that photon noise variance is small, this problem is solved by PCA, of all things. That ugly algorithm rears again its ugly head! But also this justifies things we have been hearing from the Kepler camp, that is, that a low-dimensional PCA model of lightcurves is good at describing lightcurves. And I am pleased to note that the correct generalization as the noise variance gets large is my own HMF. The day ended with Foreman-Mackey doing some experiments.